Transient three-dimensional temperature distribution in a solid irradiated by a moving Gaussian laser beam was investigated numerically by means of COMSOL Multiphysics 3.3. The investigated work-piece are simply brick-type solids. A laser source is considered moving with constant velocity along the motion direction. The solid dimension along the motion direction is assumed as semi-infinite while width and thickness are considered finite. Several different grid distributions are tested to ensure that the calculated results are grid independent. Typical parameters involved in the processes for any particular application should be evaluated, in order to optimize the material processing and forecast the solid behavior. The results are presented in terms of temperature profiles and thermal fields are given for some Biot and Peclet numbers.